Next-generation DFT-based Next-generation DFT-based quantum models for simulations of quantum models for simulations of

biocatalysisbiocatalysis

Darrin M. YorkDarrin M. York

UUniversity of niversity of MMinnesotainnesota

Minneapolis, Minneapolis, Minnesota Minnesota

USAUSA

http://http://theory.chem.umn.edutheory.chem.umn.edu

OutlineOutline

• AM1/d-PhoT model for RNA catalysisAM1/d-PhoT model for RNA catalysis

• Efficient treatment of long-range Efficient treatment of long-range electrostatics in semiempirical electrostatics in semiempirical calculationscalculations

• Improved charge-dependant Improved charge-dependant response propertiesresponse properties

• Selected applicationsSelected applications

• Study phosphate reactivity comprehensively (using small Study phosphate reactivity comprehensively (using small models) with high-level quantum models (models) with high-level quantum models (ab initioab initio and and DFT)DFT)

• Construct accurate semiempirical quantum models capable Construct accurate semiempirical quantum models capable of being used in linear-scaling electronic structure and of being used in linear-scaling electronic structure and QM/MM simulationsQM/MM simulations

• Develop improved (accurate, fast and general) models for Develop improved (accurate, fast and general) models for electrostatics, solvation and generalized solvent boundary electrostatics, solvation and generalized solvent boundary potentials.potentials.

• Investigate how to improve next-generation semiempirical Investigate how to improve next-generation semiempirical quantum models to account for charge-dependent quantum models to account for charge-dependent response properties without significant sacrifice of response properties without significant sacrifice of efficiency.efficiency.

• Validate methods with respect to known reactions in Validate methods with respect to known reactions in solution, then apply them to the important problem of RNA solution, then apply them to the important problem of RNA catalysis in a realistic system consisting of many thousands catalysis in a realistic system consisting of many thousands of particles, and simulated for many tens of nanoseconds.of particles, and simulated for many tens of nanoseconds.

……in wordsin words

Phosphates and phosphoranesPhosphates and phosphoranes

Mechanisms for phosphoryl transferMechanisms for phosphoryl transfer

O

P

O O

ROlg

O

P

O O

OlgR

O

P

O O

ROlg

O

P

O O

ROlgOnucR OnucR

O

P

O O

ROlg

O

P

O O

OnucR OnucRROlg

Dissociative

DN

Concerted

ANDN

Associative

AN+DN

QCRNAQCRNA – Online! – Online! http://theory.chem.umn.edu/QCRNAhttp://theory.chem.umn.edu/QCRNA

Molecule (2000+)Molecule (2000+) Reaction Mechanism (300+)Reaction Mechanism (300+)Giese Giese et al.,et al., J. Mol. Graph. Model. J. Mol. Graph. Model. 2525, 423 (2006)., 423 (2006).

Potential Energy SurfacePotential Energy Surface

Reaction Reaction TablesTables

Graphical Graphical InterfaceInterface

QCRNAQCRNA – Online! – Online! http://theory.chem.umn.edu/QCRNAhttp://theory.chem.umn.edu/QCRNA

Giese Giese et al.,et al., J. Mol. Graph. Model. J. Mol. Graph. Model. 2525, 423 (2006)., 423 (2006).

Phosphate isomerization Phosphate isomerization (Migration)(Migration)

Liu Liu et al., J. Phys. Chem. B, .et al., J. Phys. Chem. B, .109109, 19987 (2005); , 19987 (2005); Chem. Chem. CommunCommun.., , 3131, 3909 (2005). , 3909 (2005). Silva-Lopez Silva-Lopez et al., et al., Chem. Chem. EurEur. J.. J.,, 1111, 2081 (2005); , 2081 (2005); Mayaan Mayaan et al., et al., J. Biol. J. Biol. InorgInorg. Chem. Chem.., , 99, 807 (2004). , 807 (2004).

Range Range et al., et al., J. Am. Chem. Soc.J. Am. Chem. Soc.,, 126126, 1654 (2004)., 1654 (2004).

movie

Parameter Optimization: AM1/d MethodsParameter Optimization: AM1/d Methods

2Mol Prop

2 )()( i

DFTi

Semiiiα YYw

λλ

2)( iiw

0bλCγλ )()(2 TTraining set included a wide variety of biological phosphates and Training set included a wide variety of biological phosphates and phosphoranes, hydrogen bonded complexes, proton affinities and phosphoranes, hydrogen bonded complexes, proton affinities and reaction paths of associative and dissociative mechanisms in different reaction paths of associative and dissociative mechanisms in different charge states.charge states.

Nam Nam et al.,et al., J. Chem. Theory Comput., submittedJ. Chem. Theory Comput., submitted..

Why use a semiempirical model?Why use a semiempirical model?

It is important to note that for the ribozyme systems of interest, the It is important to note that for the ribozyme systems of interest, the details of the mechanisms remain topics of considerable debate. details of the mechanisms remain topics of considerable debate. Hence the goal is to test multiple mechanisms with a model that is Hence the goal is to test multiple mechanisms with a model that is sufficiently predictive to discern the most probable path.sufficiently predictive to discern the most probable path.

A consensus has emerged that, in certain ribozymes such as HHR and A consensus has emerged that, in certain ribozymes such as HHR and HDV, a large scale conformational change either precedes or is HDV, a large scale conformational change either precedes or is concomitant with the chemical step of the reaction.concomitant with the chemical step of the reaction.

This necessitates the use of a quantum model that is able to be used This necessitates the use of a quantum model that is able to be used with extensive conformational sampling (i.e., simulation) while providing with extensive conformational sampling (i.e., simulation) while providing an accurate description, in terms of energy, structure and charge an accurate description, in terms of energy, structure and charge distribution, along multiple mechanistic paths (i.e., not a single pre-distribution, along multiple mechanistic paths (i.e., not a single pre-determined 1-D reaction coordinate) in order to be predictive.determined 1-D reaction coordinate) in order to be predictive.

4

1i

)cR(bBi

)cR(bAiBA

AB

BAMNDOABAB

2BiAB

Bi

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R

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Modification for AM1/d-PhoT ModelModification for AM1/d-PhoT Model

If GA and GB = 0, MNDO Hamiltonian

Modified Core-Core Repulsion

Core-Core Repulsion

ABBABA RRBBAABA

MNDOAB ee1ssssZZE

4

1i

)cR(bBi

)cR(bAi

AB

BAMNDOABAB

2BiAB

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R

ZZEE

MNDO

AM1 and PM3

If GA and GB = 1, AM1 and PM3

Want a Want a dd-orbital method for hypervalent species, but one that also -orbital method for hypervalent species, but one that also describes reasonably hydrogen bonding interactions. Combine MNDO/d describes reasonably hydrogen bonding interactions. Combine MNDO/d framework with a modified core-core term similar to AM1 (and retaining framework with a modified core-core term similar to AM1 (and retaining some AM1 parameters unmodified) to build a semiempirical model for some AM1 parameters unmodified) to build a semiempirical model for phosphoryl transfer reactions: AM1/d-PhoTphosphoryl transfer reactions: AM1/d-PhoT

AM1/d-PhoT Model for Phosphoryl TransferAM1/d-PhoT Model for Phosphoryl Transfer

AM1/d-PhoT Model for Phosphoryl TransferAM1/d-PhoT Model for Phosphoryl Transfer

AM1/d-PhoT Model for Phosphoryl TransferAM1/d-PhoT Model for Phosphoryl Transfer

AM1/d-PhoT Model for Phosphoryl TransferAM1/d-PhoT Model for Phosphoryl Transfer

AM1/d-PhoT Model for Phosphoryl TransferAM1/d-PhoT Model for Phosphoryl Transfer

Reaction Energies and Barrier HeightsReaction Energies and Barrier Heights

Error*Error*Neutral RxnNeutral Rxn Monoanionic RxnMonoanionic Rxn Dianionic RxnDianionic Rxn Dissociative RxnDissociative Rxn

AM1/dAM1/d AM1AM1 PM3PM3 AM1/dAM1/d AM1AM1 PM3PM3 AM1/dAM1/d AM1AM1 PM3PM3 AM1/dAM1/d AM1AM1 PM3PM3

Reaction EnergyReaction Energy

No. RxnNo. Rxn 55 44 22 33

MSEMSE 2.072.07 -7.32-7.32 -10.78-10.78 0.840.84 -2.48-2.48 -4.94-4.94 -1.44-1.44 -9.00-9.00 -2.96-2.96 5.255.25 -23.24-23.24 -12.35-12.35

MUEMUE 2.862.86 7.397.39 10.7810.78 1.961.96 9.799.79 8.808.80 2.282.28 9.009.00 5.655.65 5.255.25 23.2423.24 12.3512.35

Activation EnergyActivation Energy

No. TSNo. TS 1313 1111 44 33

MSEMSE 0.760.76 3.483.48 -18.76-18.76 -2.91-2.91 -0.36-0.36 -12.74-12.74 -3.33-3.33 -22.58-22.58 -31.77-31.77 3.353.35 10.0810.08 -10.38-10.38

MUEMUE 3.613.61 6.626.62 18.7618.76 3.573.57 12.2312.23 16.2316.23 3.333.33 22.5822.58 31.7731.77 6.606.60 10.0810.08 10.3810.38

Relative Intermediate EnergyRelative Intermediate Energy

No. IntNo. Int 88 77

MSEMSE -1.06-1.06 -42.29-42.29 -26.61-26.61 -6.59-6.59 -42.34-42.34 -34.10-34.10

MUEMUE 2.362.36 42.2942.29 26.6126.61 6.596.59 42.3442.34 34.1034.10

*Errors are computed against “B3LYP/6-311++G(3df,2p) adiabatic energies”

Linear Free Energy RelationsLinear Free Energy Relations

TransphosphorylatiTransphosphorylation of a cyclic on of a cyclic phosphate with phosphate with enhanced leaving enhanced leaving groups.groups.

Slope of plot is the Slope of plot is the BrBrøønsted nsted correlation correlation parameter parameter ββlg lg often often used to used to characterize characterize phosphoryl transfer phosphoryl transfer reactions.reactions.

The logk values The logk values were calculated were calculated from DFT and are from DFT and are contained in contained in QCRNA.QCRNA.

Gas Phase Proton Affinity IGas Phase Proton Affinity I

B3LYP: B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)

MoleculeMolecule Ref.Ref.ErrorError

B3LYPB3LYP AM1/dAM1/d AM1AM1 PM3PM3 MNDO/dMNDO/d

HH33OO++ 165.0165.0 -1.1-1.1 3.83.8 -2.0-2.0 -11.8-11.8 5.65.6

HOHHOH 390.3390.3 0.10.1 5.45.4 20.520.5 11.311.3 30.630.6

CHCH33OHOH 381.5381.5 -2.2-2.2 2.02.0 2.72.7 -1.9-1.9 1.81.8

CHCH33CHCH22OHOH 378.2378.2 -2.2-2.2 2.92.9 4.74.7 -0.4-0.4 5.25.2

CC66HH55OHOH 350.1350.1 -2.4-2.4 -3.4-3.4 -3.1-3.1 -6.9-6.9 0.00.0

CHCH33COCO22HH 347.2347.2 -0.8-0.8 -2.7-2.7 6.16.1 0.90.9 9.69.6

P(O)(OH)(OH)(OH)P(O)(OH)(OH)(OH) 330.5330.5 -2.4-2.4 -3.4-3.4 7.67.6 15.015.0 -12.2-12.2

P(O)(O)(OH)P(O)(O)(OH) 310.6310.6 -0.1-0.1 1.51.5 20.620.6 35.135.1 -3.6-3.6

P(O)(O)(OH)(OH)P(O)(O)(OH)(OH)-- 458.9458.9 -1.1-1.1 -1.9-1.9 16.816.8 24.724.7 -2.8-2.8

P(O)(O)(O)(OH)P(O)(O)(O)(OH)2-2- 581.1581.1 -1.7-1.7 10.410.4 33.733.7 36.436.4 16.316.3

P(O)(OH)(OH)(OCHP(O)(OH)(OH)(OCH33)) 329.3329.3 0.40.4 0.30.3 7.27.2 14.914.9 -12.0-12.0

P(O)(O)(OH)(OCHP(O)(O)(OH)(OCH33))-- 454.9454.9 -1.4-1.4 0.70.7 16.516.5 22.822.8 -7.6-7.6

P(O)(OH)(OCHP(O)(OH)(OCH33)(OCH)(OCH33)) 329.4329.4 0.70.7 1.81.8 7.37.3 12.312.3 -14.1-14.1

P(O)(OH)(OCHP(O)(OH)(OCH22CHCH22O)O) 329.5329.5 -0.1-0.1 -0.2-0.2 7.67.6 11.811.8 -17.1-17.1

MSEMSE -1.0-1.0 0.90.9 9.49.4 8.58.5 -5.1-5.1

MUEMUE 1.11.1 2.42.4 9.89.8 11.011.0 11.411.4Range Range et al., Phys. Chem. Chem. Phys.et al., Phys. Chem. Chem. Phys. 7,7, 3070 (2005). 3070 (2005).

Gas Phase Proton Affinity II: Phosphorane CompoundsGas Phase Proton Affinity II: Phosphorane Compounds

MoleculeMolecule Ref.Ref.ErrorError

B3LYPB3LYP AM1/dAM1/d AM1AM1 PM3PM3 MNDO/dMNDO/d

P(OH)(OH)(OH)(OP(OH)(OH)(OH)(OHH)(OH))(OH) 351.0351.0 -0.4-0.4 3.03.0 9.09.0 8.38.3 -1.3-1.3

P(OP(OHH)(OH)(OH)(OH)(OH))(OH)(OH)(OH)(OH) 341.0341.0 -1.8-1.8 1.81.8 13.613.6 9.09.0 -8.7-8.7

P(OH)(OH)(OCHP(OH)(OH)(OCH22CHCH22O)(OO)(OHH)) 351.9351.9 -0.9-0.9 1.21.2 5.95.9 1.71.7 -11.8-11.8

P(OP(OHH)(OH)(OCH)(OH)(OCH22CHCH22O)(OH)O)(OH) 343.2343.2 -1.1-1.1 -2.5-2.5 8.08.0 -0.5-0.5 -17.4-17.4

P(OP(OHH)(OCH)(OCH22)(OCH)(OCH22CHCH22O)(OH)O)(OH) 345.2345.2 -0.7-0.7 -3.5-3.5 3.63.6 -2.3-2.3 -20.2-20.2

P(OH)(OCHP(OH)(OCH22)(OCH)(OCH22CHCH22O)(OO)(OHH)) 352.0352.0 -0.8-0.8 2.32.3 5.45.4 -0.4-0.4 -27.0-27.0

P(OP(OHH)(OH)(OCH)(OH)(OCH22CHCH22O)(OCHO)(OCH22)) 343.5343.5 -1.1-1.1 -0.7-0.7 6.26.2 -0.9-0.9 -19.5-19.5

MSEMSE -1.0-1.0 0.20.2 7.47.4 2.12.1 -15.2-15.2

MUEMUE 1.01.0 2.12.1 7.47.4 3.33.3 15.215.2

Range Range et al., Phys. Chem. Chem. Phys.et al., Phys. Chem. Chem. Phys. 7,7, 3070 (2005). 3070 (2005).B3LYP: B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)

Example: QM/MM of Di-anionic Reactions in WaterExample: QM/MM of Di-anionic Reactions in Water

-10

-5

0

5

10

15

20

25

30

35

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

EP(-)….OH(-)

DMP(-)…OH(-)

TMP(-)...OH(-)

q = R(P-Ol) - R(On-P)

Dejaegere and Karplus, JACS 1993Cox and Ramsay, Chem. Rev. 1964

Comparison with DFT and Expt. in kcal/mol

*DFT: B3LYP/6-311++G(3df,2p)

RxnRxnGasGas AquoAquo

AM1/dAM1/d DFTDFT AM1/dAM1/d ExptExpt

DMPDMP TSTS11 82.282.2 88.388.3 32.132.1 ~32~32

TS2TS2 78.778.7 87.587.5 31.531.5

ProdProd -13.1-13.1 -7.8-7.8 -3.1-3.1

EPEP TSTS 84.284.2 86.786.7 24.224.2 21~2421~24

ProdProd 30.230.2 35.935.9 -5.6-5.6

TMPTMP TSTS 86.086.0 89.089.0 28.828.8 ~32~32

ProdProd 25.625.6 29.329.3 -0.5-0.5

RxnRxnGasGas AquoAquo

AM1/dAM1/d DFTDFT AM1/dAM1/d ExptExpt

DMPDMP TS1TS1 82.282.2 88.388.3 32.132.1 ~32~32

TS2TS2 78.778.7 87.587.5 31.531.5

ProdProd -13.1-13.1 -7.8-7.8 -3.1-3.1

EPEP TSTS 84.284.2 86.786.7 24.224.2 21~2421~24

ProdProd 30.230.2 35.935.9 -5.6-5.6

TMPTMP TSTS 86.086.0 89.089.0 28.828.8 ~32~32

ProdProd 25.625.6 29.329.3 -0.5-0.5

ProblemsProblems

• Dispersion interactionsDispersion interactions

• Relative conformational energies: Relative conformational energies: sugar puckering and pseudorotation sugar puckering and pseudorotation transition statestransition states

• Proper treatment of polarizability Proper treatment of polarizability and multiple charge statesand multiple charge states

Giese Giese et al., J. Chem. Phys., et al., J. Chem. Phys., 123123, 164108 (2005)., 164108 (2005).

The Problem of Charge-dependent Response Properties The Problem of Charge-dependent Response Properties with Semiempirical Methodswith Semiempirical Methods

Atoms are of Atoms are of course an course an

extremeextreme case: case: but typically but typically

polarizabilities of polarizabilities of neutral neutral

molecules are molecules are typically off by typically off by

25%, and 25%, and anions by anions by

significantly significantly more…more…

Goal:Goal: Improve charge-dependent Improve charge-dependent response properties of semiempirical response properties of semiempirical methods without significantly methods without significantly increasing computational cost.increasing computational cost.

Possible solutions:Possible solutions:

• Reparameterize modelsReparameterize models

• Increase minimal basis-set Increase minimal basis-set representationrepresentation

• Make basis set exponents charge Make basis set exponents charge dependentdependent

DFT-based model…DFT-based model…

rdvFE 3)()(][][ rr

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Giese Giese et al., J. Chem. Phys.et al., J. Chem. Phys. 123123, 164108 (2005)., 164108 (2005).

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A Variational Electrostatic A Variational Electrostatic Projection (VEP) Method for Projection (VEP) Method for QM/MM CalculationsQM/MM CalculationsGoal:Goal: Model large-scale electrostatic effects of Model large-scale electrostatic effects of solvent-shielded macromolecular environment - solvent-shielded macromolecular environment - and and it’s linear responseit’s linear response – in hybrid QM/MM calculations – in hybrid QM/MM calculations for a fraction of computational cost of explicit for a fraction of computational cost of explicit simulationsimulation

Method:Method: Green’s function approach that Green’s function approach that involves variational projection and reduced involves variational projection and reduced dimensional mapping of surrounding solvent-dimensional mapping of surrounding solvent-shielded macromolecular environment onto shielded macromolecular environment onto the dynamical reaction zonethe dynamical reaction zone

Gregersen and York, Gregersen and York, J. Phys. Chem. B, J. Phys. Chem. B, 109109, 536-556 , 536-556 (2005).(2005).

Gregersen and York, Gregersen and York, J. Comput. Chem., J. Comput. Chem., 27,27, 103 103 (2006).(2006).

Reaction RegionReaction RegionQM active site + QM active site + MM surroundingMM surrounding(Newtonian dynamics)(Newtonian dynamics)

Buffer RegionBuffer Region(Langevin dynamics)(Langevin dynamics)

External potential External potential of solute and of solute and solventsolventStochastic Stochastic boundaryboundary

Multi-scale Quantum ModelsMulti-scale Quantum Models

Linear-scaling QM/MM-Ewald Linear-scaling QM/MM-Ewald MethodMethod

Nam Nam et al., J. Chem. Theory Comput., et al., J. Chem. Theory Comput., 11, 2 (2005)., 2 (2005).

Applications to enzymes and Applications to enzymes and ribozymesribozymes

• Hammerhead ribozymeHammerhead ribozymeBest characterized ribozyme – but complicated: Best characterized ribozyme – but complicated: role of metals, chemical/conformational steps, role of metals, chemical/conformational steps, non-inline native structurenon-inline native structure

• Hairpin ribozymeNo metal cofactor, in-line configurationNo metal cofactor, in-line configuration

General acid/base General acid/base mechanismmechanism

Tai-Sung Lee Tai-Sung Lee et al., submitted.et al., submitted.

MgMg2+2+ ion is observed to ion is observed to coordinate the O2’ of G8 coordinate the O2’ of G8 increasing it’s acidity in the increasing it’s acidity in the early TS and then migrate early TS and then migrate closer to the leaving group O5’ closer to the leaving group O5’ position of the scissile position of the scissile phosphate in the late TS.phosphate in the late TS.

Simulations help to explain the Simulations help to explain the long-standing disconnect long-standing disconnect between available structures between available structures and biochemical data (in and biochemical data (in particular, thio effect studies).particular, thio effect studies).

Early TSEarly TS Late TSLate TS

Other Projects…Other Projects…

• Parameters for RNA reactive intermeParameters for RNA reactive intermediatesdiates

• DNA bendingDNA bending

• Polarization-exchange couplingPolarization-exchange coupling

• Linear-scaling electronic structureLinear-scaling electronic structure

AcknowledgementsAcknowledgements• George GiambasuGeorge Giambasu• Dr. Tim GieseDr. Tim Giese• Yun LiuYun Liu• Dr. Evelyn MayaanDr. Evelyn Mayaan• Adam MoserAdam Moser• Dr. Kwangho NamDr. Kwangho Nam• Dr. Kevin RangeDr. Kevin Range

Funding/Resources:Funding/Resources:• University of MinnesotaUniversity of Minnesota

• NIHNIH• ACS-PRFACS-PRF

• Army High-Performance Computing Research CenterArmy High-Performance Computing Research Center• Minnesota Supercomputing InstituteMinnesota Supercomputing Institute

• Prof Bill ScottProf Bill Scott• Prof. Qiang CuiProf. Qiang Cui• Dhd Marcus ElstnerDhd Marcus Elstner• Prof. Jiali GaoProf. Jiali Gao• Prof. Walter ThielProf. Walter Thiel

• Dr. Olalla Nieto FazaDr. Olalla Nieto Faza• Dr. Francesca GuerraDr. Francesca Guerra• Dr. Carlos Silva LopezDr. Carlos Silva Lopez• Prof. Xabier LopezProf. Xabier Lopez• Dr. Anguang HuDr. Anguang Hu